Codimension-two refined estimate conjecture

Let $\mathfrak{e}(n,R)$ denote the exponent appearing in the paper's rational-point estimates for $(n,R)$-dimensional submanifolds satisfying condition (CC). In codimension $2$, the conjecture concerns the value of $\mathfrak{e}(n,2)$.

Codimension-two conjecture. For all sufficiently large even $n\in\mathbb{N}$,

$$\mathfrak{e}(n,2)=2.$$

The conjecture identifies the expected sharp exponent in the codimension-two case under (CC). The supplied text gives no resolution status or further evidence beyond the surrounding discussion, so it remains open in this record.